Most modern headrest are made on an FIP machine 'Foam in place' , the empty 'bag' of a headrest fitted to its frame is placed in a mould and filled by injection with a measured mixture of two chemicals (I won't go into the boring details) when they meet each other in the headrest bag they expend due to a chemical reaction and fill the mould. They then cure to a set texture.
After that the headrest is one piece, it is physically impossible to remove the cover from the foam inside.